{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Clock-Packing of Spheres\n",
    "\n",
    "[![Google Collab Book](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/tum-pbs/PhiFlow/blob/develop/examples/optim/Close_Packing.ipynb)\n",
    "\n",
    "This example optimizes sphere positions in order to find the maximally frustrated state, i.e. fill a limited space with as little overlap as possible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %pip install --quiet phiflow\n",
    "from phi.jax.flow import *\n",
    "# from phi.flow import *  # If JAX is not installed. You can use phi.torch or phi.tf as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a given number of spheres, we first define the domain `size` so that 5% more area is available than the spheres take up.\n",
    "Then we initialize the spheres at random points inside the periodic domain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "R = wrap([1]*64 + [vec(batch('d'), 1, .5)]*64, instance('spheres'))\n",
    "size = (math.sum(Sphere(vec(x=0, y=0), R).volume, 'spheres') * 1.05) ** .5\n",
    "x0 = math.random_uniform(instance(R), channel(vector='x,y'), high=size)\n",
    "plot(Sphere(x0, R), size=(6, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we define the loss function to be minimized.\n",
    "We penalize spheres whose distance is shorter than their combined radii."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss(x: Tensor, boundary=PERIODIC):\n",
    "    dx = boundary.shortest_distance(x, rename_dims(x, 'spheres', 'o'), size)\n",
    "    dr = math.vec_length(dx, eps=1e-8) / (R + rename_dims(R, 'spheres', 'o'))\n",
    "    return math.l2_loss(math.where((dr < 2e-4) | (dr > 1), 0, 1 - dr))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can not optimize this system using an optimizer of our choice. Here we use SciPy's `L-BFGS-B` optimizer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_packed = minimize(loss, Solve('L-BFGS-B', x0=x0)) % size\n",
    "plot(Sphere(x_packed, R), size=(6, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Φ<sub>Flow</sub> also allows us to record the intermediate states of the optimization.\n",
    "We can use these to visualize the process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "with math.SolveTape(record_trajectories=True) as solves:\n",
    "    minimize(loss, Solve('L-BFGS-B', x0=x0))\n",
    "x_trj = solves[0].x % size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x22f1b5f7a60>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(Sphere(x_trj, R), size=(8, 4), animate='trajectory', frame_time=40)"
   ]
  }
 ],
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